On the Uniform Ergodic for α-times Integrated Semigroups

被引：0

作者：

Tajmouati, A. ^{[1
]}

El Bakkali, A. ^{[2
]}

Barki, F. ^{[1
]}

Baba, M. A. Ould Mohamed ^{[1
]}

机构：

[1] Sidi Mohamed Ben Abdellah Univ, Lab Math Anal & Applicat LAMA, Fac Sci Dhar Al Mahraz, Fes, Morocco

[2] Chouaib Doukkali Univ, Fac Sci, Dept Math, El Jadida, Morocco

来源：

BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA | 2021年 / 39卷 / 04期

关键词：

Uniformly ergodic; alpha-times integrated semigroup; Generator; LAPLACE TRANSFORMS;

D O I：

10.5269/bspm.41944

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A be the generator of an alpha-times integrated semigroup (S(t))(t >= 0). We study the uniform ergodicity of (S(t)(t >= 0) and we show that the range of A is closed if and only if lambda R(lambda, A) is uniformly ergodic. Moreover, we obtain that (S(t))(t >= 0) is uniformly ergodic if and only if alpha = 0. Finally, we get that 1/t(alpha+1) integral(t)(0) S(s)ds converge uniformly for all alpha > 0.

引用

页码：9 / 20

页数：12

共 50 条

[11] On the asymptotics of n-times integrated semigroups
Gale, Jose E.
Martinez, Maria M.
Miana, Pedro J.
COMPLEX ANALYSIS AND SPECTRAL THEORY, 2020, 743 : 263 - 272
[12] UNIFORM ERGODIC-THEOREMS FOR LOCALLY INTEGRABLE SEMIGROUPS AND PSEUDO-RESOLVENTS
SHAW, SY
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 98 (01) : 61 - 67
[13] ERGODIC SEMIGROUPS OF EPIMORPHISMS
BEREND, D
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1985, 289 (01) : 393 - 407
[14] AN ERGODIC THEOREM FOR SEMIGROUPS
AKCOGLU, MA
CUNSOLO, J
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 24 (01) : 161 - &
[15] Uniform concentration inequality for ergodic diffusion processes observed at discrete times
Galtchouk, L.
Pergamenshchikov, S.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2013, 123 (01) : 91 - 109
[16] LAPLACE TRANSFORMS AND ALPHA-TIMES INTEGRATED SEMIGROUPS
HIEBER, M
FORUM MATHEMATICUM, 1991, 3 (06) : 595 - 612
[17] Some Conclusions about α-times Integrated C Semigroups
Liu, Chunjing
Song, Xiaoqiu
Wang, Tao
2010 THE 3RD INTERNATIONAL CONFERENCE ON COMPUTATIONAL INTELLIGENCE AND INDUSTRIAL APPLICATION (PACIIA2010), VOL I, 2010, : 355 - 359
[18] Trotter-kato Theorems for an α-times Integrated Semigroups
郎开禄
杨光俊
数学季刊, 1999, (03) : 11 - 16
[19] Spectral Inclusions Between α-times Integrated Semigroups and Their Generators
Tajmouati, A.
El Bakkali, A.
Ahmed, M. B. Mohamed
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2020, 38 (05): : 115 - 130
[20] Laplace Inverse Transformation for α -Times Integrated C Semigroups
Liu, Man
Yuan, XiaoMei
Yu, QingZhi
Wang, FuHong
ADVANCES IN FUTURE COMPUTER AND CONTROL SYSTEMS, VOL 1, 2012, 159 : 641 - 645

← 1 2 3 4 5 →